This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268775 #9 Jan 15 2019 09:09:38 %S A268775 4,11,26,65,148,343,766,1709,3752,8195,17746,38233,81916,174767, %T A268775 371366,786437,1660240,3495259,7340026,15379121,32156324,67108871, %U A268775 139810126,290805085,603979768,1252698803,2594876066,5368709129,11095332172 %N A268775 Number of n X 2 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once. %H A268775 R. H. Hardin, <a href="/A268775/b268775.txt">Table of n, a(n) for n = 1..210</a> %F A268775 Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4). %F A268775 Conjectures from _Colin Barker_, Jan 15 2019: (Start) %F A268775 G.f.: x*(4 + 3*x - 8*x^2 - 4*x^3) / ((1 + x)^2*(1 - 2*x)^2). %F A268775 a(n) = ((-1)^(1+n) + 2^(2+n) + ((-1)^n+2^(1+n))*n) / 3. %F A268775 (End) %e A268775 Some solutions for n=4: %e A268775 ..0..0. .0..0. .0..1. .0..1. .1..0. .0..0. .0..0. .1..0. .1..1. .0..0 %e A268775 ..0..0. .1..1. .1..0. .0..0. .0..0. .1..1. .0..0. .0..0. .0..0. .0..1 %e A268775 ..0..1. .0..0. .0..0. .1..1. .0..0. .0..0. .1..0. .0..1. .0..1. .0..0 %e A268775 ..1..0. .1..0. .1..0. .0..0. .1..0. .0..1. .1..0. .1..0. .0..0. .1..0 %Y A268775 Column 2 of A268781. %K A268775 nonn %O A268775 1,1 %A A268775 _R. H. Hardin_, Feb 13 2016